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You searched for +publisher:"University of South Africa" +contributor:("Kubeka, Amos Soweto"). Showing records 1 – 2 of 2 total matches.

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University of South Africa

1. Abdella Arega Tessema. Modeling, analysis and numerical method for HIV-TB co-infection with TB treatment in Ethiopia.

Degree: 2018, University of South Africa

In this thesis, a mathematical model for HIV and TB co-infection with TB treatment among populations of Ethiopia is developed and analyzed. The TB model includes an age of infection. We compute the basic reproduction numbers RTB and RH for TB and HIV respectively, and the overall repro- duction number R for the system. We find that if R < 1 and R > 1; then the disease-free and the endemic equilibria are locally asymptotically stable, respectively. Otherwise these equilibria are unstable. The TB-only endemic equilibrium is locally asymptotically stable if RTB > 1, and RH < 1. How- ever, the symmetric condition, RTB < 1 and RH > 1, does not necessarily guarantee the stability of the HIV-only equilibrium, but it is possible that TB can coexist with HIV when RH > 1: As a result, we assess the impact of TB treatment on the prevalence of TB and HIV co-infection. To derive and formulate the nonlinear differential equations models for HIV and TB co-infection that accounts for treatment, we formulate and analyze the HIV only sub models, the TB-only sub models and the full models of HIV and TB combined. The TB-only sub model includes both ODEs and PDEs in order to describe the variable infectiousness and e ect of TB treatment during the infectious period. To analyse and solve the three models, we construct robust methods, namely the numerical nonstandard definite difference methods (NSFDMs). Moreover, we improve the order of convergence of these methods in their applications to solve the model of HIV and TB co-infection with TB treatment at the population level in Ethiopia. The methods developed in this thesis work and show convergence, especially for individuals with small tolerance either to the disease free or the endemic equilibria for first order mixed ODE and PDE as we observed in our models. Advisors/Committee Members: Goufo, Emile Franc Doungmo (advisor), Kubeka, Amos Soweto (advisor).

Subjects/Keywords: HIV; TB; Nonstandard finite difference methods; Basic reproduction number; Stability; Co-infection

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APA (6th Edition):

Tessema, A. A. (2018). Modeling, analysis and numerical method for HIV-TB co-infection with TB treatment in Ethiopia. (Doctoral Dissertation). University of South Africa. Retrieved from http://hdl.handle.net/10500/24851

Chicago Manual of Style (16th Edition):

Tessema, Abdella Arega. “Modeling, analysis and numerical method for HIV-TB co-infection with TB treatment in Ethiopia.” 2018. Doctoral Dissertation, University of South Africa. Accessed November 22, 2019. http://hdl.handle.net/10500/24851.

MLA Handbook (7th Edition):

Tessema, Abdella Arega. “Modeling, analysis and numerical method for HIV-TB co-infection with TB treatment in Ethiopia.” 2018. Web. 22 Nov 2019.

Vancouver:

Tessema AA. Modeling, analysis and numerical method for HIV-TB co-infection with TB treatment in Ethiopia. [Internet] [Doctoral dissertation]. University of South Africa; 2018. [cited 2019 Nov 22]. Available from: http://hdl.handle.net/10500/24851.

Council of Science Editors:

Tessema AA. Modeling, analysis and numerical method for HIV-TB co-infection with TB treatment in Ethiopia. [Doctoral Dissertation]. University of South Africa; 2018. Available from: http://hdl.handle.net/10500/24851


University of South Africa

2. Toudjeu, Ignace Tchangou. Mathematical analysis of generalized linear evolution equations with the non-singular kernel derivative .

Degree: 2019, University of South Africa

Linear Evolution Equations (LEE) have been studied extensively over many years. Their extension in the field of fractional calculus have been defined by Dαu(x, t) = Au(x, t), where α is the fractional order and Dα is a generalized differential operator. Two types of generalized differential operators were applied to the LEE in the state-of-the-art, producing the Riemann-Liouville and the Caputo time fractional evolution equations. However the extension of the new Caputo-Fabrizio derivative (CFFD) to these equations has not been developed. This work investigates existing fractional derivative evolution equations and analyze the generalized linear evolution equations with non-singular ker- nel derivative. The well-posedness of the extended CFFD linear evolution equation is demonstrated by proving the existence of a solution, the uniqueness of the existing solu- tion, and finally the continuous dependence of the behavior of the solution on the data and parameters. Extended evolution equations with CFFD are applied to kinetics, heat diffusion and dispersion of shallow water waves using MATLAB simulation software for validation purpose. Advisors/Committee Members: Goufo, Emile Franc Doungmo (advisor), Kubeka, Amos Soweto (advisor).

Subjects/Keywords: Mathematical analysis; Evolution equation; Caputo-Fabrizio derivative; Diffusion equation; Fractional calculus; Non-singular kernel derivative; Fractional derivative; Solution operators; Semigroup; Well-posedness

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Toudjeu, I. T. (2019). Mathematical analysis of generalized linear evolution equations with the non-singular kernel derivative . (Masters Thesis). University of South Africa. Retrieved from http://hdl.handle.net/10500/25774

Chicago Manual of Style (16th Edition):

Toudjeu, Ignace Tchangou. “Mathematical analysis of generalized linear evolution equations with the non-singular kernel derivative .” 2019. Masters Thesis, University of South Africa. Accessed November 22, 2019. http://hdl.handle.net/10500/25774.

MLA Handbook (7th Edition):

Toudjeu, Ignace Tchangou. “Mathematical analysis of generalized linear evolution equations with the non-singular kernel derivative .” 2019. Web. 22 Nov 2019.

Vancouver:

Toudjeu IT. Mathematical analysis of generalized linear evolution equations with the non-singular kernel derivative . [Internet] [Masters thesis]. University of South Africa; 2019. [cited 2019 Nov 22]. Available from: http://hdl.handle.net/10500/25774.

Council of Science Editors:

Toudjeu IT. Mathematical analysis of generalized linear evolution equations with the non-singular kernel derivative . [Masters Thesis]. University of South Africa; 2019. Available from: http://hdl.handle.net/10500/25774

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